Polygonal Clustering Analysis Using Multilevel Graph‐Partition

Abstract

Existing methods of spatial data clustering have focused on point data, whose similarity can be easily defined. Due to the complex shapes and alignments of polygons, the similarity between non-overlapping polygons is important to cluster polygons. This study attempts to present an efficient method to discover clustering patterns of polygons by incorporating spatial cognition principles and multilevel graph partition. Based on spatial cognition on spatial similarity of polygons, four new similarity criteria (i.e. the distance, connectivity, size and shape) are developed to measure the similarity between polygons, and used to visually distinguish those polygons belonging to the same clusters from those to different clusters. The clustering method with multilevel graph-partition first coarsens the graph of polygons at multiple levels, using the four defined similarities to find clusters with maximum similarity among polygons in the same clusters, then refines the obtained clusters by keeping minimum similarity between different clusters. The presented method is a general algorithm for discovering clustering patterns of polygons and can satisfy various demands by changing the weights of distance, connectivity, size and shape in spatial similarity. The presented method is tested by clustering residential areas and buildings, and the results demonstrate its usefulness and universality. but are not limited to, watershed analysis, drought analysis, crime mapping, and spatial epidemiology (Joshi 2011). Therefore, spatial clustering analysis is a technique which is important to spatial data analysis and related applications.The spatial similarities between spatial objects are fundamental to clustering analysis, and many similarity measurements have been presented. Chameleon ) is a general algorithm exclusively defining the framework but not the similarity between polygon data; GDBSCAN (Sander et al. 1998) uses the areas of polygons or non-spatial attributes as similarities; REDCAP (Guo 2008, Guo and Wang 2011) only considers the distance of geometric properties and non-spatial attributes; Poly-SNN (Wang and Eick 2014) first approximates overlapping polygons as points, and then defines the similarity of polygons as the number of the points shared by their k-nearest neighbors. However, these works have not taken full advantage of geometric properties, and were not designed for measuring similarity of polygons, especially non-overlapping ones. That is, when polygons are disjoint or non-overlapping, geometric relationships and configurations between them, and visual cognition, will play a more important role than the existing measurements and non-spatial attributes in determining clusters. In this situation, the existing measurements can no longer work efficiently. Although some measures have been presented recently to group and generalize buildings (Li et al. 2004;Basaraner and Selcuk 2008;Yan et al. 2008; Zhang et al. 2013a, b), they are designed to handle buildings, which have more regular and simple shapes. These specific ...

An Intuitionistic Fuzzy Similarity Approach for Clustering Analysis of Polygons

“…During the process of measuring polygon similarities, the Relief-F algorithm [30] was applied, which generated the corresponding weight of each index instead of a trial-and-error methodology. Finally, the adjacent graph model containing the similarities between adjacent polygons was acquired, to which the multi-level graph partitioning approach [17] was applied to finalize the clustering. We added the evaluation approach to the final part of this section.…”

“…Distinct from the spatial properties of polygon P A o , the properties between adjacent polygons P B o were acquired differently [17]. The properties between adjacent polygons P B o were derived using…”

“…Although the categories vary widely, they are inseparable from similarities. As the similarities between spatial polygons are fundamental for clustering [17], exploring the influence of indices on similarity are abundant. The research initially only considered single properties [18], and investigations into multi properties arose later [19].…”

“…Geographical configuration and the spatial cognition theory [20] can handle polygons that have more regular and simple shapes. Additionally, work performed in [17] proposes a multi-level graph partitioning approach for clustering polygons, which can handle more generic polygons with irregular and complex shapes. The aforementioned studies accurately define spatial similarities between polygons, thus achieving better spatial clustering, indicating that similarity-based investigations that express the relation between polygons well are vital in spatial clustering.…”

Recognizing Linear Building Patterns in Topographic Data by Using Two New Indices based on Delaunay Triangulation

“…Graph-based grouping methods are the most common approaches, which in general, first model the building block as a graph in which nodes represent buildings and edges denote the adjacent relationships between buildings [12][13][14][15]. The graph is then segmented to obtain homogeneous groups by means of segmentation methods [1,16,17]. Some tracking methods can be integrated into the segmentation process to obtain linear building patterns [3,18].…”